Firstly, I would like to say that the streaming project was not a gimmick created by Weather Underground to attract users. This was a volunteer project that was started by a handful of people. WU was kind enough to dedicate a server and bandwidth to handle the 150+ audio streams that they are carrying now.
Common sense goes a long way. It should be obvious to anyone that you cannot rely on your Internet connection to provide you will must-have severe weather information that is knocking on your door. Does that mean you should not use the Internet to view pending bad weather like the latest radar images when bad weather is headed your way? When the power lines are coming down, and you lose your telephone and Internet, it is a little late to turn to the Internet for information.
For many people including myself the NWS radio coverage is very poor unless you have an external antenna. I would guess that 99% of the community where I live is not going to install a roof top antenna dedicated to NWS radio. Does that mean that they should not have the option of listening to the NWS radio via the Internet when bad weather is approaching? Of course not.
The whole point of NWS radio is early warning of pending weather and they do a pretty good job of that. Right now, our area is under a winter storm warning that is not really starting for another 24 hours. Usually there is plenty of advanced notice when bad weather is approaching. If bad weather is headed your way, and you are curious enough to listen to an Internet stream, odds are you are going to look for more information if the stream you normally listen to is down.
Like I said, common sense goes a long way. There will always be people out there that need to read the label on drain cleaner that says "Do not ingest". That being said, I do not think there is a need to inject disclaimers in to the streams or any other warnings about reliability.
Finally, if you are running the appropriate software, the bandwidth and resources consumed by streaming is minimal. I could probably running a stream on a 286 over a modem connection without a problem.